Portu scored a first-half winner on Sunday (local time) to move Girona a point ahead of Real Madrid, which won 2-1 at Las Palmas on Saturday. Madrid have a game in hand.
"This is a long-distance race," Girona coach Míchel Sanchez said.
"We are in a very nice position and we want to continue this run."
Girona were coming off a 3-2 loss at Mallorca in the Copa del Rey, a result that kept them from reaching the tournament's semi-finals for the first time and ended their 17-match unbeaten run in all competitions.
The team's only other loss this season came against Madrid at home in the league in September.
Girona have 17 wins in 22 league matches, and the competition's best attack with 52 goals. No other team has scored more than 45.
Michel's team have a tough stretch ahead, with matches against sixth-placed Real Sociedad, second-placed Madrid and fourth-placed Athletic Bilbao.
It was the third straight loss for Rafa Benitez's Celta, coming off two consecutive home defeats against Real Sociedad - one in the league and one in the Copa.
The Vigo team stayed in 17th place in the league.
There were some jeers during and after the match toward Benitez, who is in the first year of a three-year contract with Celta.
"We played against a good team that is at the top for good reason," Benitez said.
"We had our chances but couldn't capitalise on them."
Celta risked dropping into the relegation zone later Sunday, but Cadiz drew 0-0 with Athletic, and Sevilla were held to a 1-1 draw against Osasuna.
Girona conceded some chances but were in control during most of the match.
Portu found the net from inside the area with a low shot by the near post in the 20th minute.
"We have to keep going match by match," Portu said.
"We know that we have been opening a good gap to the other teams fighting for the European places, and that has to be our goal right now."
Sevilla's struggles continued with their 1-1 home draw against Osasuna, which left the team one point outside the relegation zone and prompted more jeers from their fans.
Sevilla have only one win in their past 16 league games and were coming off elimination against Atletico in the quarter-finals of the Copa del Rey.
Cadiz were unable to end their 20-game winless streak in all competitions on the debut of new coach Mauricio Pellegrino.
The scoreless home draw against Athletic kept Cadiz just inside the relegation zone.
Athletic moved to fourth place in the standings.
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